Question

Determine whether the function f(x) = 3x4 is even or odd.

The function is even because f(x) = f(−x).
The function is odd because f(x) = f(−x).
The function is even because −f(x) = f(x).
The function is odd because −f(x) = f(x).

Answer 1

Option A) The function is even because f(x) = f(−x).

Explanation:

We are given the following in the question:

`f(x) = 3x^4`

We have to check whether the given function is odd or even.

Even function:

• 
  `f(-x) = f(x)`

Odd function:

• 
  `f(-x) = -f(x)`

To check, we evaluate f(-x)

`f(x) = 3x^4\\f(-x) = 3(-x)^4 = 3(-1)^4(x)^4 = 3x^4 = f(x)`

Thus, the given function is even.

Answer 2

The function is even because f(x) = f(−x).

Explanation:

we know that

An even function is one for which

f (−x)=f(x) for all x in its domain.

An odd function is one for which

f( −x) =−f(x) for all x in its domain

In this problem we have

`f(x)=3x^(4)`

so

`f(-x)=3(-x)^(4)=3x^(4)`

therefore

f (x)=f(-x) for all x in its domain.

Is a even function